engine cut off while driving, wouldnt start up

With 100,000 miles on it, my 05 liberty renegade 3.7L V6 died on me shortly after leaving my home. Mind you this is in Alaska and it was a cold snap day in the 10-20 degree area. I figured the battery might need some charging so before I left my house I let it run for about 5 minutes. I was going through a roundabout and the engine just cut off as I got to exit the roundabout. I pulled over as it was rolling and had to turn the wheel with more force because my power steering was out. All the electronics were still on like the radio and my lights and everything, so I look down at my display and there was a red oil light illuminated, as well as a new check engine light. I didn't see any fluid on the road in my trails, in or before the roundabout. And I checked my oil levels and everything seemed to be fine. I was thinking maybe the battery was bad or maybe even the alternator? I'm no expert but that's what came to mind. I tried to turn the key to see if it would start in any chance but i got the clicking sound as i held the key turned. So I stood outside in the cold with jumper cables in my hand waving people down and one very nice person stopped to help. As we hooked up the cables, I gave it a try and turned the key to see that my jeep was trying to turn over now (as opposed to getting the clicking sound) and it would not fire. He gave me a ride back to my house which wasn't far and I ended up towing my jeep home later that day. Seeing as the battery might've been one of the issues, I bought a new one and installed it at home. The car started right up of course, but I'm afraid to drive the car anywhere as it might just do the same thing and I'll have to tow it again. You guys think it could be the alternator? Or maybe some sort of air/fuel/something cloggage? I need help